by Researching a cosmic mystery like dark matter has its drawbacks. On the one hand, it is exciting to be on the path to what could be a profound scientific discovery. On the other hand, it is difficult to convince people that it is worth studying something that is invisible, untouchable and apparently made of something completely unknown.
While the vast majority of physicists find the evidence for dark matter’s existence compelling, some continue to investigate alternatives, and views in the press and public are considerably more divided. The most common response I get when talking about dark matter is, “isn’t this just something physicists made up to make the math work?”
The answer to that may surprise you: yes! In fact, everything in physics is designed to make the math work.
When I first got into science, what excited me was the possibility of learning an ultimate truth about the universe. Stephen Hawking once described cosmology as an attempt to “know the mind of God”.
But while that characterization is inspiring, physics in practice is not built around ultimate truth, but rather the constant production and refinement of mathematical approximations. It is not just because we will never have perfect precision in our observations. It is fundamental that the whole point of physics is to create a model universe in mathematics – a set of equations that remain true when we plug in numbers from observations of physical phenomena.
For example, Newton’s second law of motion, which states that force equals mass times acceleration, is a mathematical model that tells us that if we measure the force exerted on an object, in appropriate units, we should get the same number as the product of the object’s mass and acceleration it experiences when exposed to that power.
In Einstein’s version of gravity, general relativity, the equations become far more complicated, but the goal of the exercise is the same. There is always a level of abstraction built into the effort because what allows us to make predictions or design new technologies is a set of equations that can be written down and calculated, not a philosophical discussion about the nature of reality.
This level of abstraction is particularly evident in particle physics, because the existence or non-existence of a single particle on a subatomic scale is a rather fuzzy notion. The equations that describe the motion of an electron through space do not actually include a particle at all, but rather an abstract mathematical object called a wave function that can spread out and disturb itself.
Is it ever true to say that an electron is “real” when it is in motion? If we believe that electrons are real things, have we just made up the wave function to make the math work? Absolutely – that was actually the whole point. We couldn’t make the equations work if the electron was a solid, isolated particle, so we invented something that wasn’t, and then the numbers started to make sense.
It may be that in the future we find a solution that we prefer to a wave function, and we abandon that concept altogether. But if we do, it will be because the math stopped working: we’ll have an experimental or observational result that doesn’t add up when we plug the data into our current equations. So, if we do our job right, we will find a new set of equations that better describe the behavior of the electron, and we will give these equations names and conceptual analogies and textbooks will be written saying ‘this is what really happens’.”
A scientist’s conception of what is really happening is always driven by mathematics. Before it was accepted that the Earth orbits the Sun, astronomers used epicycles—small orbital loops—to describe planetary motions in an Earth-centered system. This construction is often used, somewhat unfairly, as a prime example of “making things up to make the math work” go wrong.
Although it is true that we left epicycles in the 17th centuryth century, it was mathematics that made us do it. Newton’s equations of universal gravitation and Einstein’s theory of general relativity aren’t made of stronger stuff than the old equations of epicyclic motion—all these frameworks are just symbols on a page—but they fit the observations better and make predictions easier, so we use them as the foundation for our abstract model universe.
Dark matter, dark energy, cosmic inflation, black hole singularities, and all the other hypothetical inhabitants of our current cosmology may seem less real than falling apples or electricity or fluid flow because we don’t experience them in everyday life, but from a physicist’s perspective, they are all equally good fodder for mathematical abstraction.
While the way we observe something determines what kind of data points we can use, ultimately all we do is make the math work. We certainly hope that all this calculation gives us a better description of reality, but the mind of God is best left to the philosophers; we don’t have an equation for it.
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